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11.3 & 11.7 Notes

Added Apr 29, 2015 •

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if you were absent or you just need to go back over this this is 11.3 and 4 minutes field in perimeter and area of similar figures remember that a similar figure is same shape but a different size so they are proportional the sides have the same ratio and the angles are all Prince and these were the ways that we proved and Figures were similar in the past not remember that if there are similar all their sides have the same a show and their perimeters have that exact same ratio so if I can Kris all the sides by multiple of to the perimeter is going to increase by a multiple of 2 also if you double everything the perimeter doubles ossip but the area does not go up at that same rate it goes up at a different rate if two polygons are similar with the links of the corresponding sides in the right in the ratio of a to B so that's there a tabby then the area is going to be a squared to be squared so basically for every you just Square everything so if you look an example one have triangle ABC ABC and triangle jkl jkl know if you noticed a bee were the first two in they were the first two so Abby is going to go with JK so that it's going to match up with that 12 the nine is going to match up with the 6th so if I find the ratio shaded to unshaded shaded would be the 12 unshaded would be the 8th that matchup or the 9 and the 6 so if I do the 9 for six that reduces the three over to so 9 to 6 is 3 / 212 - 8 is 3/2 so that's the ratio of the Shaded to the unshaded sides the turn will have the exact same ratio but the area will be this ratio squared so Square the three get nine square that get force of 9/4 that does not reduce so this is your ratio for the area that means that if we go back up to the problem song about up here where if I double everything the perimeter doubles but the area doesn't just double it will be that squared so too is 44 times larger than the other one  okay so look at example number 2  you buy two singer pieces of aluminum window screening one is 15 ft long and it cost $135 the other is similar in shape but it's too the screen is sold by the square foot that's important what is the cost of the longer roll now your first thing you're in want to do is 15 - 135 and I need to ask however this is 15 ft - 135 and it's sold by the square foot so you're saying feet and square feet and you're making your ratio out of two things that are not equal so what you need to do is find the ratio of the sides we know they're similar ones 15 + 1 is 20 what's a 15 over 20 is 3 over for that reduces this is the ratio of your sides okay or your perimeter basic soda fun area ratio you would take this in squared 3 squared as 9 for square to 16 and that is your area ratio this is in square feet this is in single feet so since this is sold by the square foot I need to set my ratio equal to that okay so the 15 feet is 130 that's the shorter one so see you're going to match up the 1:35 with the 9th - 9/16 as a ratio here equals 135 over X cross multiply you're going to get $240 so the 20-foot is 240 and the 15 ft is 135 can you were billboard is 12 ft by 20 ft 27 ft long so there's your 27 and 12 as smaller billboard is similar so here's our smaller ones there is a smaller billboard is 144 find the height of the smaller billboard here now we don't have the wit all we have is the height show me on this area now there's several ways you can do it but if you'll find the area here cuz we have the length in the wet that's too. 24 for the area we can find the area ratio because we know both areas so full put these together 324 / 144 I think this is the easiest one down here 3/4 / 144 that reduces to 9/4 so the area ratio is 9 for now what would be the side ratio so this is the area ratio the side ratio take the square root bouquet of each of these the square root of 9 is 3 the square root of 4 is too because remember you square the side ratio to get the area go to undo that you take the square root and then you can set up a ratio because you know the X and the 12 matchup but those are single units side ratio single you so we do 3/2 equals 12 / x + 3 is the larger one so 12 is the larger so 12 is on top cross multiply get x equals 8 up here we know this ratio we put those over there squared so if we make our ratio here we can just Square it that do the other way in you cross multiply divide by 3 24 x squared got to take the square root and you still get 8 so there's two ways to do that 11.7 is geometric probability now it's probability like anything else what you want over the total that's there like the marbles if you have red and marbles in you want to Red marble you put how many red marbles are there over the total number of marbles there in that will give you the probability probability is the probability of Anna that is measure it's a measure of the likelihood that that event will occur no geometric probability is the same thing but it's a ratio that involves a geometric sure such as link or area so if you look at this  probability in link let's just talk about link first and then we'll do area let's say I have that number line right there okay so what is the probability that if I picked a point at random off of this line off of line when I be that it would be between C and D on the line what's the probability that if I picked a point random on this whole thing that it would end up between CND we want C or D so the length of CD goes on top and the length of the whole thing goes on bottom this notation is for probability the P stands for probability whatever is in the parentheses is what you want the probability of we want to know if K is on CD so here's an example  down here that we news pictures from the probability that a point chosen randomly on ad so we won't Lee want a daddy and that is 25 on the given Line 6 pressure sir as a fraction a decimal in percent so what's the problem bility that it will land on a sea whale from a to c -15 to 5 is 2080 is level 5 so 20 over 25 is 4/5 that's 80% or .8 what's the probability that it will be on BC b2c is 10 so 10 out of 25 is tooth is .4 or 40% now the other thing is probability and area so what's the probability that a point K picked at random will be in the Shaded region M on plane P so the probability that K is in region M you would do that of the Shaded area over the area of the total think now when I do the area of the total thing that is the whole plane you don't surf what's that out or added or anything that's the whole plane P so look at this example right here use area to find a geometric probability find the probability that a point chosen at random in the figure lies in the Shaded region express your answer as a percent the first of all this right here is your shaded region so the big one is a rectangle and  what would the Shaded region itself is the rectangle and you need to subtract out that semicircle okay so the big one the rectangle the total is just eight times six link times width that's 48k no it's fun the Shaded we know that's the whole thing is 48 we need to subtract out half of a circle so find the area of the whole circle Pi R Squared this is 6 so the radius is 3 + 3 to make 6 so pie times 3 squared is 28.3 now we only want half of that Circle so divide that by 2 and you get 14 point  13 so go back down here like your rectangle 48 subtract the half circle 14-point in you left with 33.87 that's the Shaded region so you would put the Shaded region on top the whole rectangle on bottom and divide that in you get .706 if you change that to a percent move cancel two places you get 70.6% so remember it's that area that you want on top over the total area that's

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11.3 & 11.7 Notes

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